It is the inherent nature of all things that they are a compilation of two different and distinct things. It is axiomatic that these two things are space and value. The value of any given thing being what it is, while the space is what it occupies.

It is true that, abstract or otherwise numbers are a thing, therefore they must also contain a compilation of space and value. It is an axiomatic truth that space is the labeling of quantities of dimensions. It is an axiomatic truth that value is the labeling of quantities of existence, other than dimensions.

It is an axiomatic truth that space and value exist in one of two forms. So that any given quantity of space or value is first labeled as defined or undefined. It is reasonable to say that any given number, that has had both its quantities of space and value labeled as undefined, requires no further question as to it's nature. If however a given number, has had both its quantities of space and value labeled as defined, it is then necessary to further define the given quantities. That is to say what is the nature of the space and value's that are defined.

There are four axiomatic steps in the further defining of a defined quantity of space and value. First it is that, after a given quantity of space and value is labeled as defined, a symbol is given to identify the amount of quantities given. Second it is that the given amounts of defined space and value are labeled as finite or infinite. Third it is that the given amounts of defined space and value, that are finite or infinite, are labeled as small or large. Fourth it is that the given amounts of defined space and value, that are finite or infinite, small or large, are labeled as positive or negative.

It is the case that all forms of the defining of quantities of space and value, are from the perspective of our humanity. This then shows that there is a collection of only four kinds of numbers. That is there are numbers that possess an undefined space and an undefined value. Otherwise represented as a ( Uv + Us ). Such a number not requiring further defining. There are numbers that possess a defined value and a defined space. Otherwise represented as a ( Dv + Ds ). Such a number requiring further defining. There are numbers that possess a defined value and an undefined space. Otherwise represented as a ( Dv + Us ). There are numbers that possess an undefined value and a defined space. Otherwise represented as a ( Uv + Ds ).

It is reasonable to say that natural numbers have both their quantities of space and value labeled as defined. That is that a natural number is a ( Dv + Ds ). It is then through the process of further defining, that a natural number such as 2 is labeled as having ( 2Dv + 2Ds ). The symbol 2 then is the symbol identifying the amounts of quantities contained. It is then that the given quantities are labeled as finite. Otherwise represented as a ( 2DvF + 2DsF ). It is then that the given quantities are labeled as large. Otherwise represented as a ( 2DvFL + 2DsFL ). It is then that a positive is assigned to the compilation of space and value, and it is so on for any natural number.

It is also the case that fractions are labeled as a ( Dv + Ds ). That is any given fraction has both its quantities of space and value labeled as defined. So that such a number as .2 is labeled as ( 2DvFS + 2DsFS ). Then a positive is assigned to the compilation of space and value. Additionally a fractional symbol may replace the decimal symbol.

It is also the case that infinite numbers are labeled as a ( Dv + Ds ). So that such a number as 2infinite is defined as a ( 2DvIL + 2DsIL ). As well as fractional infinites such as .2infinite. Which is labeled as ( 2DvIS + 2DsIS ). Then a positive is assigned to both compilations of space and value, and it is so on for any infinite or fractionally infinite number.

Remaining are numbers that are a ( Uv + Ds ) and numbers that are a ( Dv + Us ). Such numbers do not necessarily require further defining. As an undefined quantity of space or value composites the given number. So then such numbers can only be limitedly defined relative to the given defined quantity. If then a number possess a defined value and an undefined space, the sum is then relative to the defined value. So that such a number as ( Dv + Us ) is then a 1 relative. Otherwise represented as a 1r.

If then a number possess an undefined value and a defined space, the sum is then relative to the defined space. So that such a number as a ( Uv + Ds ) is then a zero. As no quantity of value is defined, and as one quantity of space is defined. The space of zero is clearly defined on any number line. The equation ( 1 + (-1) ) proves this in that, if zero did not occupy a defined space on the number line, then the equation would equal (-1), and not zero.

It is the case in multiplication and division, that neither number given is an actual number. Not in the fashion that each symbol contains both space and value. It is that one symbol is representing a value, and that one symbol is representing a space. It is the case that in multiplication the labeling of the given symbols as space or value in a specific order is not necessary. The sum yielded is always the same.

It is the case that in division the labeling of the given symbols as space or value in a specific order changes the sum that is yielded. So that as an axiom the first given symbol is labeled as value, while the second given symbol is labeled as space.

It is then that in multiplication the given value is placed additionally into the given spaces. Then all values are added in all spaces. It is then that in division the given value is placed divisionally into all given spaces. Then all values are subtracted except one.

So that in the equation ( 2 x 0 ), there is a given defined value of ( 2DvFL ), that is placed additionally into the given defined space of ( Ds ). Then all values are added in all spaces. This process then yields the number 2.

Where as the equation ( 0 x 2 ), there is a given undefined value of ( Uv ), that is placed additionally into the defined space of ( 2DsFL ). Then all values are added in all spaces. This process then yields the number zero.

So then in the equation ( 2 / 0 ), there is a defined value of ( 2DvFL ), that is placed divisionally into the defined space of ( Ds ). Then all values are subtracted except one. This process then yields the number 2.

Where as the equation ( 0 / 2 ), there is an undefined value of ( Uv ), that is placed divisionally into the defined space of ( 2DsFL ). Then all values are subtracted except one. This process then yields the number zero.

It is possible that further defining of the given defined value of a relative number, and the given defined space of a zero, is applicable and necessary.

Yes, I see my mistake. Of course an equal sign with a sum is required for it to actually be an equation. Surly I think you still understood my meaning. Surly it was not necessary to repeat the same thing for each one. Surly you have something to say in reply to the idea rather than the "grammar" as it were.

Philostotle wrote:Yes, I see my mistake. Of course an equal sign with a sum is required for it to actually be an equation. Surly I think you still understood my meaning. Surly it was not necessary to repeat the same thing for each one. Surly you have something to say in reply to the idea rather than the "grammar" as it were.

Nice....now that the assault on my grammar and spelling is done...(memorization is a facet of intelligence, and the least of which) can we have some sort of critical thinking assault on the idea it self.....again you will have to pardon any miss spelling.

The criticism that first arose in my mind is that even if physical things are composed of space and value, the leap of faith that all other abstract 'things' are also being composed of space and value cannot be accomplished solely by the word 'thing.' If there were different words that only applied to physical things on the one hand and to abstract things on the other--with no word like 'thing' in common--the argument that physical and abstract things share common qualities might sound hollow.

However, the criticism may be too gross. It could be said--as a counter-argument--that numbers certainly occupy a space in the scheme of all concepts and that numbers have their own unique essence, or value, in comparison to other such things, and even to similar things.

In art, one of the techniques of learning to draw is to draw the spaces, not the objects. In essence, the combination of space and matter define the sensory world around us, and it has been argued that mathematics is merely the abstract extrapolations and creative combinations of humanity's sensed facts about reality.

I became interested in your arguments when I saw them as a potential paradigm for defining the 'texture' of a pattern, i.e., by defining a given pattern as the flow and tide of ranges of substance and breadths of space.

I am looking for a new math for gambling, one that describes and extrapolates from situations as they presently are, not as they would be as an infinite average. To the extent that a pattern is recognizable and persists, we can presume a lack of randomness to one degree or another, and it would be nice to have a simple game logic that extrapolates the favorability or unfavorability of a game from a recognizable pattern that persists.

This is a question about the nature of Mathematics as a language. The question is very simple, as the thread name suggests, but I’ll expand my own perception of it here and so it would be helpful if someone can leave a few comments.

Is mathematics relative or absolute? My insight developed as follows…; If Mathematics as language was invented by us it was definitely invented based on the observations of the physical space and laws on our planet. To simplify; we can find one thing in common between 2 yellow stones on one location and then 2 blue stones on another – the fact that there are 2 stones in each group. So number 2 is the commonality. If we add these 2 groups of stones together then we get 4 stones in a group. Same goes with almost any other similar situation.

However, one exception would be that if we have 2 protons in one location and 2 antiprotons in another, surely we can still count 4 protons but they can never coexist together in contact with each other. So why is it that 2+2 is still equal to 4, wouldn’t that statement be meaningless if we tried to count the particles by using mathematics without actually knowing that they annihilate?

Now imagine that yellow and blue stones could never have coexisted (for the purpose of the argument) in the same group in contact with each other, how would we be able to say that 2 yellow stones and 2 blue stones would be 4 stones? Wouldn’t we as humans have developed a different rule for the situation and say that 2+2 = 0? I came to conclude that the problem can be fixed by marking one group of particles with an opposite charge (which is what is generally done), but doesn’t this then become merely an adjustment (or contamination) in mathematics? Why did we have to add physical characteristics as extra notations to everything that didn’t make sense otherwise? These issues have me wondering whether mathematics as we know it can be entirely different in other parts of the universe(s)… so if someone can shed some light it would be great.gclub